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The use of the multi-cumulant tensor analysis for the algorithmic optimisation of investment portfolios

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  • Domino, Krzysztof

Abstract

The cumulant analysis plays an important role in non Gaussian distributed data analysis. The shares’ prices returns are good example of such data. The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability. Such algorithm is based on the Alternating Least Square method and involves the simultaneous minimisation 2’nd–6’th cumulants of the multidimensional random variable (percentage shares’ returns of many companies). Then the algorithm was tested during the recent crash on the Warsaw Stock Exchange. To determine incoming crash and provide enter and exit signal for the investment strategy the Hurst exponent was calculated using the local DFA. It was shown that introduced algorithm is on average better that benchmark and other portfolio determination methods, but only within examination window determined by low values of the Hurst exponent. Remark that the algorithm is based on cumulant tensors up to the 6’th order calculated for a multidimensional random variable, what is the novel idea. It can be expected that the algorithm would be useful in the financial data analysis on the world wide scale as well as in the analysis of other types of non Gaussian distributed data.

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  • Domino, Krzysztof, 2017. "The use of the multi-cumulant tensor analysis for the algorithmic optimisation of investment portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 267-276.
    • Handle: RePEc:eee:phsmap:v:467:y:2017:i:c:p:267-276
    DOI: 10.1016/j.physa.2016.10.042
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    1. Giovani L. Vasconcelos, 2004. "A Guided Walk Down Wall Street: an Introduction to Econophysics," Papers cond-mat/0408143, arXiv.org.
    2. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    3. Domino, Krzysztof, 2012. "The use of the Hurst exponent to investigate the global maximum of the Warsaw Stock Exchange WIG20 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 156-169.
    4. Bertrand Maillet & Emmanuel Jurczenko, 2006. "Multi-moment Asset Allocation and Pricing Models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00308990, HAL.
    5. Bertrand Maillet & Emmanuel Jurczenko, 2006. "Introduction to Multi-moment Asset Allocation and Pricing Models," Post-Print hal-00308991, HAL.
    6. Czarnecki, Łukasz & Grech, Dariusz & Pamuła, Grzegorz, 2008. "Comparison study of global and local approaches describing critical phenomena on the Polish stock exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6801-6811.
    7. Grech, Dariusz & Pamuła, Grzegorz, 2008. "The local Hurst exponent of the financial time series in the vicinity of crashes on the Polish stock exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4299-4308.
    8. Schwert, G William & Seguin, Paul J, 1990. "Heteroskedasticity in Stock Returns," Journal of Finance, American Finance Association, vol. 45(4), pages 1129-1155, September.
    9. Bertrand Maillet & Emmanuel Jurczenko, 2006. "Multi-moment Asset Allocation and Pricing Models," Post-Print hal-00308990, HAL.
    10. Bertrand Maillet & Emmanuel Jurczenko, 2006. "Introduction to Multi-moment Asset Allocation and Pricing Models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00308991, HAL.
    11. Domino, Krzysztof, 2011. "The use of the Hurst exponent to predict changes in trends on the Warsaw Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 98-109.
    12. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    13. Akgiray, Vedat, 1989. "Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts," The Journal of Business, University of Chicago Press, vol. 62(1), pages 55-80, January.
    14. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    15. Juan C. Arismendi & Herbert Kimura, 2014. "Monte Carlo Approximate Tensor Moment Simulations," ICMA Centre Discussion Papers in Finance icma-dp2014-08, Henley Business School, University of Reading.
    16. Domino, Krzysztof & Błachowicz, Tomasz, 2014. "The use of copula functions for modeling the risk of investment in shares traded on the Warsaw Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 77-85.
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    1. Domino, Krzysztof, 2020. "Multivariate cumulants in outlier detection for financial data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).

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